Question: Evaluate the definite integral. $\int^{10}_{5}\big(3x+3\big)\,dx =$
Explanation: First, use the power rule: $\int^{10}_{5}\big(3x+3\big)\,dx ~=~\frac32 x^2+3x\Bigg|^{{10}}_{5}$ Second, plug in the limits of integration: $\big[\frac32\cdot{10}^2+3\cdot{10}\big]-\big[\frac32\cdot{5}^2+3\cdot{5}\big] = 150+30 -37.5-15 = 127.5$. The answer: $\int^{10}_{5}\big(3x+3\big)\,dx ~=~ 127.5$